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Kaspar Sakmann

Publications and source records attributed to Kaspar Sakmann.

At least 19 recordsLinked to original sources
arXiv2024

Fast yet Safe: Early-Exiting with Risk Control

Scaling machine learning models significantly improves their performance. However, such gains come at the cost of inference being slow and resource-intensive. Early-exit neural networks (EENNs) offer a promising solution: they accelerate inference by allowing intermediate layers to exit and produce a prediction early. Yet a fundamental issue with EENNs is how to determine when to exit without severely degrading performance. In other words, when is it 'safe' for an EENN to go 'fast'? To address this issue, we investigate how to adapt frameworks of risk control to EENNs. Risk control offers a distribution-free, post-hoc solution that tunes the EENN's exiting mechanism so that exits only occur when the output is of sufficient quality. We empirically validate our insights on a range of vision and language tasks, demonstrating that risk control can produce substantial computational savings, all the while preserving user-specified performance goals.

cs.LG↗
arXiv2024

Adaptive Bounding Box Uncertainties via Two-Step Conformal Prediction

Quantifying a model's predictive uncertainty is essential for safety-critical applications such as autonomous driving. We consider quantifying such uncertainty for multi-object detection. In particular, we leverage conformal prediction to obtain uncertainty intervals with guaranteed coverage for object bounding boxes. One challenge in doing so is that bounding box predictions are conditioned on the object's class label. Thus, we develop a novel two-step conformal approach that propagates uncertainty in predicted class labels into the uncertainty intervals of bounding boxes. This broadens the validity of our conformal coverage guarantees to include incorrectly classified objects, thus offering more actionable safety assurances. Moreover, we investigate novel ensemble and quantile regression formulations to ensure the bounding box intervals are adaptive to object size, leading to a more balanced coverage. Validating our two-step approach on real-world datasets for 2D bounding box localization, we find that desired coverage levels are satisfied with practically tight predictive uncertainty intervals.

cs.CV↗
arXiv2023

Max-Rank: Efficient Multiple Testing for Conformal Prediction

Multiple hypothesis testing (MHT) frequently arises in scientific inquiries, and concurrent testing of multiple hypotheses inflates the risk of Type-I errors or false positives, rendering MHT corrections essential. This paper addresses MHT in the context of conformal prediction, a flexible framework for predictive uncertainty quantification. Some conformal applications give rise to simultaneous testing, and positive dependencies among tests typically exist. We introduce $\texttt{max-rank}$, a novel correction that exploits these dependencies whilst efficiently controlling the family-wise error rate. Inspired by existing permutation-based corrections, $\texttt{max-rank}$ leverages rank order information to improve performance and integrates readily with any conformal procedure. We establish its theoretical and empirical advantages over the common Bonferroni correction and its compatibility with conformal prediction, highlighting the potential to strengthen predictive uncertainty estimates.

stat.ME↗
arXiv2023

Anomaly-Aware Semantic Segmentation via Style-Aligned OoD Augmentation

Within the context of autonomous driving, encountering unknown objects becomes inevitable during deployment in the open world. Therefore, it is crucial to equip standard semantic segmentation models with anomaly awareness. Many previous approaches have utilized synthetic out-of-distribution (OoD) data augmentation to tackle this problem. In this work, we advance the OoD synthesis process by reducing the domain gap between the OoD data and driving scenes, effectively mitigating the style difference that might otherwise act as an obvious shortcut during training. Additionally, we propose a simple fine-tuning loss that effectively induces a pre-trained semantic segmentation model to generate a ``none of the given classes" prediction, leveraging per-pixel OoD scores for anomaly segmentation. With minimal fine-tuning effort, our pipeline enables the use of pre-trained models for anomaly segmentation while maintaining the performance on the original task.

cs.CV↗
arXiv2023

Certified Defences Against Adversarial Patch Attacks on Semantic Segmentation

Adversarial patch attacks are an emerging security threat for real world deep learning applications. We present Demasked Smoothing, the first approach (up to our knowledge) to certify the robustness of semantic segmentation models against this threat model. Previous work on certifiably defending against patch attacks has mostly focused on image classification task and often required changes in the model architecture and additional training which is undesirable and computationally expensive. In Demasked Smoothing, any segmentation model can be applied without particular training, fine-tuning, or restriction of the architecture. Using different masking strategies, Demasked Smoothing can be applied both for certified detection and certified recovery. In extensive experiments we show that Demasked Smoothing can on average certify 64% of the pixel predictions for a 1% patch in the detection task and 48% against a 0.5% patch for the recovery task on the ADE20K dataset.

cs.CV↗
arXiv2018

Conserving symmetries in Bose-Einstein condensate dynamics requires many-body theory

We explain from first principles why satisfying conservation laws in Bose Einstein condensate dynamics requires many-body theory. For the Gross-Pitaevskii mean-field we show analytically and numerically that conservation laws are violated. We provide examples for angular momentum and linear momentum conservation. Arbitrarily large violations occur despite negligible depletion and interaction energy. For the case of angular momentum we show through extensive many-body simulations how the conservation law can be gradually restored on the many-body level. Implications are discussed.

cond-mat.quant-gas↗
arXiv2015

Single shot simulations of dynamic quantum many-body systems

The single-particle density is the most basic quantity that can be calculated from a given many-body wave function. It provides the probability to find a particle at a given position when the average over many realizations of an experiment is taken. However, the outcome of single experimental shots of ultracold atom experiments is determined by the $N$-particle probability density. This difference can lead to surprising results. For example, independent Bose-Einstein condensates (BECs) with definite particle numbers form interference fringes even though no fringes would be expected based on the single-particle density [1-4]. By drawing random deviates from the $N$-particle probability density single experimental shots can be simulated from first principles [1, 3, 5]. However, obtaining expressions for the $N$-particle probability density of realistic time-dependent many-body systems has so far been elusive. Here, we show how single experimental shots of general ultracold bosonic systems can be simulated based on numerical solutions of the many-body Schrödinger equation. We show how full counting distributions of observables involving any number of particles can be obtained and how correlation functions of any order can be evaluated. As examples we show the appearance of interference fringes in interacting independent BECs, fluctuations in the collisions of strongly attractive BECs, the appearance of randomly fluctuating vortices in rotating systems and the center of mass fluctuations of attractive BECs in a harmonic trap. The method described is broadly applicable to bosonic many-body systems whose phenomenology is driven by information beyond what is typically available in low-order correlation functions.

cond-mat.quant-gas↗
arXiv2014

Universality of Fragmentation in the Schrödinger Dynamics of Bosonic Josephson Junctions

The many-body Schrödinger dynamics of a one-dimensional bosonic Josephson junction is investigated for up to ten thousand bosons and long times. The initial states are fully condensed and the interaction strength is weak. We report on a universal fragmentation dynamics on the many-body level: systems consisting of different numbers of particles fragment to the same value at constant mean-field interaction strength. The phenomenon manifests itself in observables such as the correlation functions of the system. We explain this universal fragmentation dynamics analytically based on the Bose-Hubbard model. We thereby show that the extent to which many-body effects become important at later times depends crucially on the initial state. Even for arbitrarily large particle numbers and arbitrarily weak interaction strength the dynamics is many-body in nature and the fragmentation universal. There is no weakly interacting limit where the Gross-Piatevskii mean-field is valid for long times.

cond-mat.quant-gas↗
arXiv2014

Single shot three-dimensional imaging of dilute atomic clouds

Light field microscopy methods together with three dimensional (3D) deconvolution can be used to obtain single shot 3D images of atomic clouds. We demonstrate the method using a test setup which extracts three dimensional images from a fluorescent $^{87}$Rb atomic vapor.

physics.atom-ph↗
arXiv2013

Excitation spectra of many-body systems by linear response: General theory and applications to trapped condensates

We derive a general linear-response many-body theory capable of computing excitation spectra of trapped interacting bosonic systems, e.g., depleted and fragmented Bose-Einstein condensates (BECs). To obtain the linear-response equations we linearize the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method, which provides a self-consistent description of many-boson systems in terms of orbitals and a state vector (configurations), and is in principle numerically-exact. The derived linear-response many-body theory, which we term LR-MCTDHB, is applicable to systems with interaction potentials of general form. From the numerical implementation of the LR-MCTDHB equations and solution of the underlying eigenvalue problem, we obtain excitations beyond available theories of excitation spectra, such as the Bogoliubov-de Gennes (BdG) equations. The derived theory is first applied to study BECs in a one-dimensional harmonic potential. The LR-MCTDHB method contains the BdG excitations and, also, predicts a plethora of additional many-body excitations which are out of the realm of standard linear response. In particular, our theory describes the exact energy of the higher harmonic of the first (dipole) excitation not contained in the BdG theory. We next study a BEC in a very shallow one-dimensional double-well potential. We find with LR-MCTDHB low-lying excitations which are not accounted for by BdG, even though the BEC has only little fragmentation and, hence, the BdG theory is expected to be valid. The convergence of the LR-MCTDHB theory is assessed by systematically comparing the excitation spectra computed at several different levels of theory.

cond-mat.quant-gas↗
arXiv2012

Exact quantum dynamics of bosons with finite-range time-dependent interactions of harmonic type

The exactly solvable quantum many-particle model with harmonic one- and two-particle interaction terms is extended to include time-dependency. We show that when the external trap potential and finite-range interparticle interaction have a time-dependency the exact solutions of the corresponding time-dependent many-boson Schrödinger equation are still available. We use these exact solutions to benchmark the recently developed multiconfigurational time-dependent Hartree method for bosons (MCTDHB) [Phys. Rev. Lett. {\bf 99}, 030402 (2007), Phys. Rev. A {\bf 77}, 033613 (2008)]. In particular, we benchmark the MCTDHB method for: (i) the ground state; (ii) the breathing many-body dynamics activated by a quench scenario where the interparticle interaction strength is suddenly turned on to a finite value; (iii) the non-equilibrium dynamic for driven scenarios where both the trap- and interparticle-interaction potentials are {\it time-dependent}. Excellent convergence of the ground state and dynamics is demonstrated. The great relevance of the self-consistency and time-adaptivity, which are the intrinsic features of the MCTDHB method, is demonstrated by contrasting the MCTDHB predictions and those obtained within the standard full configuration interaction method spanning the Fock space of the same size, but utilizing as one-particle basis set the fixed-shape eigenstates of the one-particle potential. Connections of the model's results to ultra-cold Bose-Einstein condensed systems are addressed.

cond-mat.quant-gas↗
arXiv2012

Dynamics and symmetries of a repulsively bound atom pair in an infinite optical lattice

We investigate the dynamics of two bosons trapped in an infinite one-dimensional optical lattice potential within the framework of the Bose-Hubbard model and derive an exact expression for the wavefunction at finite time. As initial condition we chose localized atoms that are separated by a distance of $d$ lattice sites and carry a center of mass quasi-momentum. An initially localized pair ($d=0$) is found to be more stable as quantified by the pair probability (probability to find two atoms at the same lattice site) when the interaction and/or the center of mass quasi-momentum is increased. For initially separated atoms ($d \neq 0$) there exists an optimal interaction strength for pair formation. Simple expressions for the wavefunction, the pair probability and the optimal interaction strength for pair formation are computed in the limit of infinite time. Whereas the time-dependent wavefunction differs for values of the interaction strength that differ only by the sign, important observables like the density and the pair probability do not. With a symmetry analysis this behavior is shown to extend to the $N$-particle level and to fermionic systems. Our results provide a complementary understanding of the recently observed [Winkler \textit{et al.}, Nature (London) \textbf{441}, 853 (2006)] dynamical stability of atom pairs in a repulsively interacting lattice gas.

cond-mat.quant-gas↗
arXiv2012

How does an interacting many-body system tunnel through a potential barrier to open space?

The tunneling process in a many-body system is a phenomenon which lies at the very heart of quantum mechanics. It appears in nature in the form of alpha-decay, fusion and fission in nuclear physics, photoassociation and photodissociation in biology and chemistry. A detailed theoretical description of the decay process in these systems is a very cumbersome problem, either because of very complicated or even unknown interparticle interactions or due to a large number of constitutent particles. In this work, we theoretically study the phenomenon of quantum many-body tunneling in a more transparent and controllable physical system, in an ultracold atomic gas. We analyze a full, numerically exact many-body solution of the Schrödinger equation of a one-dimensional system with repulsive interactions tunneling to open space. We show how the emitted particles dissociate or fragment from the trapped and coherent source of bosons: the overall many-particle decay process is a quantum interference of single-particle tunneling processes emerging from sources with different particle numbers taking place simultaneously. The close relation to atom lasers and ionization processes allows us to unveil the great relevance of many-body correlations between the emitted and trapped fractions of the wavefunction in the respective processes.

cond-mat.quant-gas↗
arXiv2011

Recursive formulation of the multiconfigurational time-dependent Hartree method for fermions, bosons and mixtures thereof in terms of one-body density operators

The multiconfigurational time-dependent Hartree method (MCTDH) [Chem. Phys. Lett. {\bf 165}, 73 (1990); J. Chem. Phys. {\bf 97}, 3199 (1992)] is celebrating nowadays entering its third decade of tackling numerically-exactly a broad range of correlated multi-dimensional non-equilibrium quantum dynamical systems. Taking in recent years particles' statistics explicitly into account, within the MCTDH for fermions (MCTDHF) and for bosons (MCTDHB), has opened up further opportunities to treat larger systems of interacting identical particles, primarily in laser-atom and cold-atom physics. With the increase of experimental capabilities to simultaneously trap mixtures of two, three, and possibly even multiple kinds of interacting composite identical particles together, we set up the stage in the present work and specify the MCTDH method for such cases. Explicitly, the MCTDH method for systems with three kinds of identical particles interacting via all combinations of two- and three-body forces is presented, and the resulting equations-of-motion are briefly discussed. All four possible mixtures of fermions and bosons are presented in a unified manner. Particular attention is paid to represent the coefficients' part of the equations-of-motion in a compact recursive form in terms of one-body density operators only. The recursion utilizes the recently proposed Combinadic-based mapping for fermionic and bosonic operators in Fock space [Phys. Rev. A {\bf 81}, 022124 (2010)] and successfully applied and implemented within MCTDHB. Our work sheds new light on the representation of the coefficients' part in MCTDHF and MCTDHB without resorting to the matrix elements of the many-body Hamiltonian with respect to the time-dependent configurations. It suggests a recipe for efficient implementation of the schemes derived here for mixtures which is suitable for parallelization.

quant-ph↗
arXiv2011

Number fluctuations of cold spatially split bosonic objects

We investigate the number fluctuations of spatially split many-boson systems employing a theorem about the maximally and minimally attainable variances of an observable. The number fluctuations of many-boson systems are given for different numbers of lattice sites and both mean-field and many-body wave functions. It is shown which states maximize the particle number fluctuations, both in lattices and double-wells. The fragmentation of the states is discussed, and it is shown that the number fluctuations of some fragmented states are identical to those of fully condensed states.

cond-mat.quant-gas↗
arXiv2011

Optimal time-dependent lattice models for nonequilibrium dynamics

Lattice models are abundant in theoretical and condensed-matter physics. Generally, lattice models contain time-independent hopping and interaction parameters that are derived from the Wannier functions of the noninteracting problem. Here, we present a new concept based on time-dependent Wannier functions and the variational principle that leads to optimal time-dependent lattice models. As an application, we use the Bose-Hubbard model with time-dependent Wannier functions to study a quench scenario involving higher bands. We find a separation of times scales in the dynamics and show that under some circumstances the multi-band nonequilibrium dynamics of a quantum system can be obtained essentially at the cost of a single-band model.

quant-ph↗
arXiv2009

Quantum dynamics of attractive versus repulsive bosonic Josephson junctions: Bose-Hubbard and full-Hamiltonian results

The quantum dynamics of one-dimensional bosonic Josephson junctions with attractive and repulsive interparticle interactions is studied using the Bose-Hubbard model and by numerically-exact computations of the full many-body Hamiltonian. A symmetry present in the Bose-Hubbard Hamiltonian dictates an equivalence between the evolution in time of attractive and repulsive Josephson junctions with attractive and repulsive interactions of equal magnitude. The full many-body Hamiltonian does not possess this symmetry and consequently the dynamics of the attractive and repulsive junctions are different.

cond-mat.quant-gas↗